In particular, I remain convinced that the concept of an airborne fraction (AF) of carbon emissions is entirely erroneous; it is unsafe to base policy on the idea that chemical processes and ecosystems will take up a fixed proportion of annual carbon emissions.

As well as my last blog entry (and the two previous discussions it references), I have been engaged in an extended email dialogue with the Climate Philosopher, who has added a question to my original post on the BERN model:

“Do you think all of the processes depend on the level in the atmosphere dCO2(Outflow)/dt = a(CO2 – p) where a & p are constants. This would be my simple understanding.
– ie is BERN *completely* wrong?

Or are there some processes that are BERN-like e.g. equilibrium with the upper oceans so that dCO2(Outflow)/dt = a1(CO2 -p) + b(dCO2(Inflow)/dt)

I’d like it that the simple model (that bern is completely wrong) was the valid one.”

The answer to the question posed in the second paragraph is “yes”, although the “or” beginning the sentence is logically incomplete and, in this case, misplaced – we cannot categorise “all” carbon uptake processes in any single way.

Here’s a numerical summary of what I think is happening (based on IPCC AR4 data, all figures very approx.):

“Surface water” is (by definition) in eq’m with atmosphere. According to the IPCC (Fig. 7.3), such water holds 18GtC more than the pre-industrial level. i.e. approx. 0.16GtC per ppm increase in atmospheric CO2 (that is ~18GtC divided by the 110ppm increase – from 280ppm to 390ppm – in atmospheric CO2 levels).

This process of “uptake by re-equilibration” (the Climate Philosopher’s b(dCO2(Inflow)/dt) ) is therefore weak – accounting for ~0.3GtC per year (0.16GtC/ppm from above times an annual increase in atmospheric CO2 of a bit under 2ppm) increase in CO2 held in surface waters.

But there is a turnover of ~10% of ocean surface water p.a. This accounts for the Climate Philosopher’s other term: a(CO2 -p).

In this process the ocean exchanges carbon between surface and the deep ocean. Even though, this process releases carbon (because there is more in the deep ocean than the surface waters), it releases less now than before industrialisation, because the descending waters hold more carbon than before.

By the overturning process, the deep ocean therefore currently takes up 1.8GtC p.a. more than before industrialisation.

The total extra carbon uptake of 1.8 (from overturning) + 0.3 (because of 2ppm/yr increase) = 2.1GtC/yr, a good fit with published data based on observations.

Sanity check: a letter to Nature by Peter Cox (I can’t access more than the synopsis either) suggests the ocean *could* take up 5GtC/yr under BAU by 2100 implying that by then there will be 50GtC more than the pre-industrial level in surface water. The CO2 in the atmosphere would therefore be 280ppm + 50/0.15 = 280+330 = ~600ppm. Sounds about right.

And the consequences are…

1. It’s hands-up time. The idea in my original post that “it appears that removal by the oceans is indeed saturated (AR4, p.26 & elsewhere)” is wrong (and too pessimistic). The AR4 reference is to the data on ocean uptake over the last 25 years which has increased from about 1.8 to 2.2GtC/year (although these figures are very rough estimates). The point is that, whilst annual emissions have increased significantly since 1980, the atmospheric level, which is dominant in determining the ocean uptake rate, has not increased so much.

2. The idea that a fixed proportion of annual anthropogenic carbon emissions remains in the atmosphere (i.e. that the AF remains constant) is also false. My original post is correct on this point, if a little pessimistic on the ability of the ocean to take up CO2. Curiously, whilst trying to find a bit more information about the BERN model, I came across this recent paper by Terenzi and Khatiwala (pdf). I have to say I’m rather disappointed there’s no reference to my original post, since I noted from a bit of ad hoc modelling that the AF only remains roughly constant “while CO2 emissions and atmospheric levels are increasing at a fairly steady rate.” Terenzi and Khatiwala note that:

“Specifically, our results suggest that both the quasi-constancy of AF over the past half-century, and its particular numerical value of ~50%, are essentially a consequence of exponentially growing emissions with a nearly-constant growth rate of 1/40th per year.”

So basically, as T&K point out, policies assuming a constant AF are quite possibly misguided! Both T&K (loads of equations) and myself (back of an envelope) reach the conclusion that the “constant” AF is an artefact, entirely data-dependent, a mere coincidence!!

3. I still can’t relate the BERN carbon cycle model to the real world. It appears to assume atmospheric carbon will return asymptotically to equilibrium following the emission of a pulse of carbon. Deriving an AF in this way makes little sense for several reasons:

Different feedbacks have different effects over different time periods. For example: after some centuries elevated levels of dissolved CO2 in the oceans will affect the oceanic ability to take up more CO2; warming of the land (fast) and oceans (slow) will at some point affect CO2 uptake; etc. I haven’t even considered uptake of carbon by the biosphere, but the response will likely not resemble a chemical equilibrium, since secondary ecosystem responses will modulate carbon uptake. The process will also differ considerably between the oceans and land.

The natural carbon cycle is not in equilibrium. Rather, because of the different time-periods of various feedbacks, it oscillates, giving us the ice age cycle (in resonant response to Milankovitch forcings).

You simply can’t model individual years’ carbon emissions according to the BERN model, since we’re already out of equilibrium, by more and more each year. This observation, in itself, casts considerable doubt on the “constant AF” conception.

It does rather seem to me that the idea that “if industrial emissions ceased tomorrow” atmospheric carbon would progressively decline to approach an equilibrium level is entirely suspect. Furthermore, when we consider possible scenarios of future annual carbon emissions we have a more complex situation, perhaps more of a bifurcation: if our emissions continue to increase rapidly, the AF will increase, even without positive carbon cycle feedbacks (only the relatively tiny amount of carbon taken up by re-equilibration of the ocean surface waters is proportionate to emissions; other carbon uptake processes are proportionate, at best, to the difference between current and pre-industrial CO2 levels); whereas, if we decrease our annual emissions, natural processes will help us, and the AF will actually decrease – or even go negative.

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Just had a thought; maybe a difference equation is a more flexible way of expressing the dependency of the outflow term, because a difference equation could in principle deal with intermediate equilibria between the instant and the pre-industrial.

e.g. something like:
a1(CO2(t) – CO2(t-1000)) + b(CO2(t)-CO2(t-1))

Where the deep oceans have a time constant of 1000 years and the shallow oceans equilibrate over 1 year.

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